The most-watched race of Tuesday's primaries — the Republican Senate primaries between Tea Party challenger Chris McDaniel and longtime Mississippi Senator Thad Cochran — seems to be headed for a run-off as of Wednesday morning, meaning that it's likely McDaniel and Cochran will have to put their names on the ballot once again three weeks from now on June 24.

The Associated Press reports that, unofficially, 98 percent of the votes have been counted and neither candidate has gained the simple majority needed to win outright. McDaniel is in the lead, with 49.6 of the vote. Cochran has 48.9.

There's a second possible run-off coming from Mississippi based on the current vote count: thanks to what Politico called a "ballot snafu," the Republican primary for Mississippi's fourth district is still too close to call. Rep Steven Palazzo currently has 50.5 percent of the vote with 100 percent of precincts reporting. His challenger Gene Taylor, a former conservative Democrat who lost his seat to Palazzo in 2010 and is now running as a Republican, trails with 43 percent. But apparently, an unspecified number of ballots from Harrison county — which leans towards Taylor — need to be recounted by hand because elections officials "delivered the wrong boxes" to several precincts. So maybe that recount will cut Palazzo below his majority threshold, which he's currently holding with an 800 vote margin.

We'll update this post with more information on the Mississippi contests as it's available. In the mean time, other results from Tuesday's primary races in eight states are available here.

Update Wednesday 12:28 a.m.: Speaking to a crowd of supporters, Chris McDaniel is clearly happy with tonight's results, even if they do seem headed for a runoff once all the votes are (eventually) counted. "Whether it’s tomorrow or whether it’s three weeks from tonight, we will stand victorious," he said. Meanwhile:

Update Wednesday 12:06 a.m.: With a little over 95 percent of the votes counted, neither Senator Thad Cochran nor his challenger, Chris McDaniel, have enough of a share to avoid a run-off election in three weeks. McDaniel is hovering at about 49.4 percent, with Cochran behind him at about 49 percent.

However: not all of the votes are in. And things have gone especially slowly in a couple Mississippi counties tonight:

Under Mississippi's rules, one of the candidates will have to get more than 50 percent of the vote in order to avoid a runoff. With about 60 percent of the votes in, Cochran had 50.7 percent, with McDaniel not too far behind at 47.6, according to the AP. (Update, 10:50 p.m.: with 84 percent of the vote in, McDaniel now leads slightly over Cochran, 50.1 percent to 48.3 percent) Whoever wins the primary — either now or in a runoff rematch a few weeks from now — will face off against Travis Childers, who won the Democratic primary for the same seat.

The Cochran-McDaniel face-off is just one of two close races in Mississippi tonight. Former Rep. Gene Taylor, who served as a Democrat but is now running as a Republican, was slightly leading over the man who removed him from office in 2010: Steven Palazzo. With 60 percent in, neither had met the needed threshold to avoid a runoff.

Here are some other results from last night:

In South Dakota, Republican Mike Rounds and Democrat Rick Weiland will face off in November for the Senate seat vacated by retiring Democrat Tim Johnson. As the Washington Post notes, Rounds is favored to win the general elections.

In Alabama, Republican Rep. Mike Rogers fended off a challenger to secure the nomination for his re-election, and incumbent Governor Robert Bentley was also renominated. Sen. Jeff Sessions was renominated unopposed for November.

In New Jersey Republican Steve Lonegan — the guy who lost to Cory Booker for the U.S. Senate — lost to Republican Tom MacArthur in the primaries for retiring Republican Rep. Jon Runyan.

In Iowa, Joni Ernst (i.e. the candidate who talked about pig castration in a campaign ad about making Washington "squeal") easily won the Republican primary in the Senate race for retiring Democratic Senator Tom Harkin, according to the AP.

In Montana's race to replace Sen. Max Baucus — another retiring Democrat that could be an opportunity for the GOP — Rep. Steve Daines won the Republican nod for November. He'll face the winner of the Democratic primary, who will likely be newly-appointed Senator John Walsh, Roll Call reports.